A Poisson-based formulation for frictional impact analysis of multibody mechanical systems with open or closed kinematic chains

Analysis of frictional impact in a multibody mechanical system requires a friction model capable of correct detection of all possible impact modes such as sliding, sticking, and reverse sliding. Conventional methods for frictional impact analysis have tither shown energy gain or nor developed for jointed mechanical system, and especially not for closed-chain multibody systems. This paper presents a general formulation for the analysis of impact problems with friction in both open- and closed-loop multibody mechanical systems. Poisson's hypothesis is used for the definition of the coefficient of restitution, and thus the energy gains inherent with the use of Newton's hypothesis are avoided. A canonical form of the system equations of motion rising Cartesian coordinates and Cartesian momenta is utilized. The canonical momentum-balance equations are formulated and solved for the change in the system Cartesian momenta using an extension of Routh's graphical method for the normal and tangential impulses. The velocity jumps are calculated by balancing the accumulated system momenta during the contact period. The formulation is shown to recognize all modes of impact; i.e., sliding, sticking, and reverse sliding. The impact problems are classified into seven types, and based on the pre-impact system configuration and velocities, expressions for the normal and tangential impulses are derived for each impact type. Examples including the tip of a double pendulum impacting the ground with some experimental verification, and the impact of the rear wheel and suspension system of an automobile executing a very stiff bump are analyzed with the developed formulation.